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Vol. 11 No. 06 (2024)
International Multidisciplinary Journal for Research & Development

Articles

CYLINDRICAL FUNCTIONS AND THEIR APPLICATIONS TO SOLVING PROBLEMS OF MATHEMATICAL PHYSICS

Published 2024-06-19

  • Bogdan Anna Mihaylovna

Bogdan Anna Mihaylovna
Fergana State University, faculty of mathematics and informatics, area of mathematics, student of the third course.

Abstract

The article is devoted to the study of cylindrical functions and their application in problems of mathematical physics. Cylindrical functions are widely used in modeling physical processes in cylindrical regions, such as wave propagation, thermal conductivity, and electromagnetic fields. The paper discusses the main types of cylindrical functions, including Bessel functions, modified Bessel functions and other special functions. The differential equations defining cylindrical functions and their basic properties are studied. Examples are given of the use of cylindrical functions to solve the Laplace equation, the Helmholtz equation and the heat equation in cylindrical coordinates. Particular attention is paid to the issues of numerical modeling of cylindrical functions and the features of their implementation in software. Thus, this work represents a comprehensive study of cylindrical functions and their use in problems of mathematical physics.

Keywords

Cylindrical functions, mathematical physics, Laplace’s equation, Helmholtz equation, heat equation, Bessel equation, modified Bessel equation, Bessel functions, modeling of physical processes, numerical methods.

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